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"I've never had a horn that warbles on low B or C. "

I find that many horns, especially sopranos, will warble there if the mouthpiece is pulled out a long way. Some of the newer Selmer models seem particulary fussy about this.
 

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Gordon (NZ) said:
... from thread "Eft".

I presume that means that if an overtone is slightly out of tune with the fundamental, then it produces a slow 'beat frequency' that presents itself as a pulsating volume change.

Seeing "inharmonicity" refers to this very out-of-tuneness, perhaps this clarifies the statement made by Dr Wolfe in post #1.

What I wonder about my argument there, is that the does not seem much variation between saxes in the frequency of that pulsing we call burble. Surely they would not all have the same acoustic design weakness.
I don't think so. Beats happen when two frequencies are close together. It doesn't happen with harmonics. If you have a 440 Hz tone and one at 444 you'll get a 4 Hz beat. But one at 440 and another at 884 is a difference of 444 Hz, which won't do it.

Toby
 

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It may be that because the first harmonic is unstable-not a true octave-as soon as the tone breaks from the fundamental and jumps up it hits not the octave but some poor facsimile thereof, and then drops immediately back to the fundamental, where the cycle starts anew. Basically if you wanted to try to reproduce it artificially it would be necessary not to jump between octaves, but between the fundamental and some seriously compromised octave composed of horrible cross fingerings to make it unstable...

Toby
 

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Interesting experiment, John. I am no expert, but let me put in a couple of cents worth of speculation.

First, it is a shame that we don't have numbers on your graphs for the x axis, which is clearly frequency. I don't know what the first smaller peak is (could be an artifact of some kind), but I am assuming that the largest peak (in the lefthand graph) at around 0.25 is the fundamental. The second large peak at around 0.4 would be the octave, and that peak just above 0.5 might be the 12th.

If that is the case it looks like the warble is indeed the octave--you lose the fundamental and the first partial becomes predominant, with a significant increase in the second partial and increases in some of the higher partials. What is important to note is that there is no pitch shift of the peaks: the second graph shows the same peak positioning as the first.

I suggest you try using the same mpc and play the octave with the octave key and compare that with graph 2. I think you will find that they are quite similar, and any differences might give you some clues as to why the octave warble is not stable and drops back to the fundamental.

Just a thought on your question: since the reed behavior plays a role on the pitch and the harmonic structure of the note, by adjusting the embouchure in a way that emphasizes the fundamental at the expense of the first partial it might be possible to somewhat stabilize the note so that it does not have a tendency to jump up to the octave. This might also involve slightly shifting some of the partials in frequency as well--you could check this by varying you embouchure somewhat in a long tone and checking the graphs...

Going further in the opposite direction, it is clearly easy to adjust the embouchure so that you are sounding the octave without using the octave key (to the consternation of many a beginner).

I will be interested in seeing accurate before/after graphs using the acousticoil. If it actually does reduce motorboating we should carefully check the graphs for differences in both pitch and amplitude in peaks to see if we can find anything that might help explain the effect of the coil.

Toby
 

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kymarto said:
I don't think so. Beats happen when two frequencies are close together. It doesn't happen with harmonics. If you have a 440 Hz tone and one at 444 you'll get a 4 Hz beat. But one at 440 and another at 884 is a difference of 444 Hz, which won't do it.

Toby
First, they don't need to be close together to 'beat'. If we play third octave notes ona flute, a third apart in a duet, we often get unpleasant low notes sounding, which are the 'beat' frequency betwen the two third octave notes.

"But one at 440 and another at 884 is a difference of 444 Hz, which won't do it."

OK, we get a diffeerence of 444, which is sounding alongside the 440, so we still get a 4 hz sounding.
 

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Gordon (NZ) said:
First, they don't need to be close together to 'beat'. If we play third octave notes ona flute, a third apart in a duet, we often get unpleasant low notes sounding, which are the 'beat' frequency betwen the two third octave notes.
Indubitably. Consider that if you are playing an F# at 1480 Hz and an A at 1760 the beat frequency will be 280 Hz, which is basically a C#. Any beat frequency is the difference between two tones being sounded, but the resulting frequency has to be quite slow to result in a perceived "beat" (probably under 20 Hz or it sounds like a continuous tone).

Gordon (NZ) said:
"But one at 440 and another at 884 is a difference of 444 Hz, which won't do it."

OK, we get a diffeerence of 444, which is sounding alongside the 440, so we still get a 4 hz sounding.
You have made an error here, I believe. If I am not mistaken, the 4 Hz beat you posit, being the "beat of a beat", will be very weak, nothing at all like that present between two primary notes 4 Hz apart. You can easily test this if you have a frequency oscillator, and I think you will find that I am right. If not please let me know immediately ;)

Anyway, all this is moot. It's clear from John's spectrographs that there is a definite octave jump when motorboating, as the peaks do not shift frequency at all, only amplitude.

Toby
 

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kymarto said:
Interesting experiment, John. I am no expert, but let me put in a couple of cents worth of speculation.

First, it is a shame that we don't have numbers on your graphs for the x axis, which is clearly frequency. I don't know what the first smaller peak is (could be an artifact of some kind), but I am assuming that the largest peak (in the lefthand graph) at around 0.25 is the fundamental. The second large peak at around 0.4 would be the octave, and that peak just above 0.5 might be the 12th.
I agree. This is one of the weakness of my spectrum analysis software I need to address.
kymarto said:
If that is the case it looks like the warble is indeed the octave--you lose the fundamental and the first partial becomes predominant, with a significant increase in the second partial and increases in some of the higher partials.
I agree that the "visual" speaks to this effect, but what you actually hear is not an octave jump, but the pitch dropping approximately a half step.
kymarto said:
What is important to note is that there is no pitch shift of the peaks: the second graph shows the same peak positioning as the first.
Great observation!
kymarto said:
I suggest you try using the same mpc and play the octave with the octave key and compare that with graph 2. I think you will find that they are quite similar, and any differences might give you some clues as to why the octave warble is not stable and drops back to the fundamental.
Great idea! Your other observations have generated a lot of ideas to try as well.
kymarto said:
I will be interested in seeing accurate before/after graphs using the acousticoil. If it actually does reduce motorboating we should carefully check the graphs for differences in both pitch and amplitude in peaks to see if we can find anything that might help explain the effect of the coil.
I'm working on that right now. Thanks for you expert help with this.

John
 

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"Anyway, all this is moot. It's clear from John's spectrographs that there is a definite octave jump when motorboating, as the peaks do not shift frequency at all, only amplitude."

Is not an octave 'jump" the result of one frequency reducing in volume and another increasing. Isn't that what beat frequencies are all about, as one wave interacts with another, with the puklsing in volume being the "beat"? (I never mentioned frequency "shift".)
 

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The problem could be a result of a "lazy" key opening when it should not when playing the lower notes as mentioned earlier. The tone holes at the top of the tube are critical for the proper functioning of the low notes. Another thought could be the reed vibrationing from the mouthpiece which could point to an inconsistent embouchre.

Some time ago I read that Selmer Paris offerred, as an option, grooves (not sure if rifled or parallel) inside the neck. This was described as improving projection.

Question for your amusement: What do saxophone and oboe have in common? :)
 

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Gordon (NZ) said:
"Anyway, all this is moot. It's clear from John's spectrographs that there is a definite octave jump when motorboating, as the peaks do not shift frequency at all, only amplitude."

Is not an octave 'jump" the result of one frequency reducing in volume and another increasing. Isn't that what beat frequencies are all about, as one wave interacts with another, with the puklsing in volume being the "beat"? (I never mentioned frequency "shift".)
A beat frequency is not generally related to either of the two frequencies which produce it (which is, as you point out, created by synthesis of cancellation/reinforcement effects of two waves interacting). Of course it is possible that, given the right two frequencies, you create a beat frequency that has an exact mathematical relationship with one of the two frequencies which produce it, so that it is a partial of that frequency, which would generally only change the timbral character of the tone, and not be perceived as a distinct note. One of the main characteristics of beat notes is that they are always lower than the two frequencies that produce them, as they are based on the division and not the multiplication of frequencies.

You know, of course, that one of the tricks used by pipe organ builders to create bass notes with short pipes was to take two pipes of rather high frequency and detune them just enough to create an in-tune bass note out of the beat frequency. Neat, huh?

Anyway, how could the motorboating be a beat frequency when it arises out of a single note? (Or am I not understanding your comments...)

Toby
 

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jbtsax said:
I agree that the "visual" speaks to this effect, but what you actually hear is not an octave jump, but the pitch dropping approximately a half step.
John
Ah, this is interesting. What happens between graph 1 and graph 2 ? Do the peaks shift at all, dropping back to the positions we see at the "top" and "bottom" of the motorboating effect? It might also be useful to plot one full cycle with very small time divisions--to see the rise and fall of the effect and how it changes over time.

What does it sound like when you slow it way, way down? If you can correlate audial phases with their allied spectrographs you might get some interesting insight into psychoacoustics or some sort of pure acoustic phenomenon: I have no idea why an octave jump should be perceived as semitone drop (if it is indeed an octave jump...)

Toby
 

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kymarto said:
...Anyway, how could the motorboating be a beat frequency when it arises out of a single note? (Or am I not understanding your comments...)....
I was just making suggestions to explore, as to cause, reather than just description, following the acoustician'[s mention of inharmonicity. But I acknowldege my level of ignorance is high.

I don't regard a note with inharmonic overtones as a single note. :)

I also acknowledge that all manner of acoustic illusions occur, for example us 'hearing' (i.e. inferring) a fundamental for the lowest notes of a piano, when there apparently is almost none there.
 

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Gordon (NZ) said:
I was just making suggestions to explore, as to cause, reather than just description, following the acoustician'[s mention of inharmonicity. But I acknowldege my level of ignorance is high.

I don't regard a note with inharmonic overtones as a single note. :)

I also acknowledge that all manner of acoustic illusions occur, for example us 'hearing' (i.e. inferring) a fundamental for the lowest notes of a piano, when there apparently is almost none there.
Gordon,

I'm not trying to get on your case, only pointing out that in my (non-expert) opinion what you propose is on the far edge of possibility. Any note (with inharmonic overtones or not) can be considered a single note insofar as it is not possible for a note with a single fundamental to create a beat. Even if the first partial is slightly out of tune and is of large amplitude, it is still almost or slightly more than an octave apart from the fundamental, and unless we are talking about a fundamental of around 20 Hz or less the interference relationship of the octave with the fundamental will not produce a perceptible "beat".

Toby
 

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First, as I understand it, the first overtone for an oboe is louder than the fundametal, so overtones can indeed be of significant volume. I have not bothered investigating fro a sax.

OK. I play A440. The first overtone, with its inharmonicity, plays at 882. This creates a beat ('difference') frequency with the fundamental of 882 - 440 = 442.
442 - 440 = a beat frequency of 2 hertz. (I assume these sorts of complexities do in fact go on.) Isn't this 2 hz the frequency at which the fundametnal waxes and wanes?

Whether that is perceptible or not, I have no idea.
Whether or not it has anything to do with the low note sax burble, I have no idea.
But a acoustician who knows miles more than I do, mentioned inharmonicity in his explanation. I am merely pondering as to why inharmonicity could be a factor.

Edited, because my figures were crap.
 

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Wow, where do you guys GET this stuff? I had no idea so many acoustical engineers and physicists played sax. Please keep it coming, even though I don't understand most of it.
 

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Toby mentions "mode-locking". This is a vital concept that is often
not factored in. (See below for some references.)

If one is using a non-linear source, i.e. a reed, then the partials will
pull together to lock to a common periodic-wave, the perceived pitch. The partial that has the highest amplitude will have the greatest influence.

Therefore, in a normal reed woodwind, there is NO INHARMONICTY in the
sound! (I verified this with fft's on my own instruments.)

Question:

How do the sax techs know whether a note that is off-pitch is due to
the fundamental being off or whether the note is being pulled off
by the bores "natural" (unaffected by non-linearity) out-of-tune
partials? Do they use a linear source, like an earphone or ear plug
to excite the instrument in order to indicate natural horn inharmonicity?
If so, do they leave the reed on?
In the first case, should one address the tone hole? In the second case, should one address the bore?

jim

References:

Arthur H. Benade, "Fundamentals of Musical Acoustics": pgs 395, 471, 501.

Fletcher/Rossing, "The Physics of Musical Instruments": pgs 143, 422.
 

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Discussion Starter · #38 ·
Hi Jim. Thanks for keeping this thread alive. I'm hoping we can generate more interest in acoustics is this forum. I have read the pages you made reference and I am having difficulty understanding the point you want to make with regard to mode locking and its effect on inharmonicity.

I'm afraid that I have to disagree with you that there is no inharmonicity present in woodwind instruments. Benade refers to "misaligned resonances" which I believe is the same principle and makes this statement on p. 446 of FMA.

Anything that works against the maintenance of oscillation (such as the reduction of the heights of air-column resonance peaks by frictional or radiation damping, or the misalignment of these resonances so that they fail to set up strongly cooperative oscillatory regimes) requires the player to operate the reed on the more steeply falling portion of its flow control curve. In order to produce this increased steepness, the musician is required to exert more effort in his playing, so as to provide a combination of increased blowing pressure and greater embouchure tension. This explains why instruments having either heavily damped or grossly misaligned resonances are usually described as "hard blowing," and why the player is likely to find them physically tiring to play.

It is a common observation that a really fine instrument with accurately aligned resonances can be played comfortably with a reed that is considerably stiffer than can be used on a less well aligned instrument, even if the heights of the various resonance peaks are the same in both cases.
John
 

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jtbsax said:
inharmonicity present in woodwind instruments
I might be recalling one of my college classes on non-linear differential equations (I'm not kidding - I might be recalling it), in which we studied the resonances of things like drum heads. They had resonances that were non-harmonically related to the fundamental. Tapered bore tubes are like that. Flutes and clarinets need not apply.
 

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Hi John,

I think that when Benade and other theorists refer to “air-column resonances” they are talking about the natural bore resonances of the instrument when excited by a linear source or theoretically calculated. The non-linear reed pulls these resonances together to form a pitch that has harmonic partials.
Of course, the more the “air-column resonances” are misaligned, the more energy is lost in the reed and the more energy is required to play in tune because the pitch is being pulled by the air-column enharmonicity.

Having harmonic air-column resonances is, perhaps, the most important characteristic of a fine woodwind.

jim
 
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